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Generating functions for stoichiometry and structure of single- and double-layer sheet-silicates

Part of: Foundations in mineralogy and crystallography

Published online by Cambridge University Press:  02 January 2018

Frank C. Hawthorne
Frank C. Hawthorne*
Affiliation:
Department of Geological Sciences, University of Manitoba, Winnipeg, Manitoba R3T 2N2, Canada
*
*E-mail: frank_hawthorne@umanitoba.ca
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Abstract

Two-dimensional nets may be used to generate the stoichiometry and structure of single-layer and double-layer sheet-silicate minerals. Many sheet-silicate minerals are based on the 3-connected plane nets 63, 4.82, (4.6.8)2(6.82)1and (52.8)1(5.82)1, and some more complicated nets, e.g. (5.6.7)4(5.72)1(62.7)1, (4.122)2(42.12)1, (52.8)1(5.62)1(5.6.8)2(62.8)1,have one or two representative structures. Many complicated sheet-silicate minerals are based on sheets of 2-, 3- and 4-connected tetrahedra that may be developed from 3- and 4-connected plane nets by a series of oikodoméic operations on 3- or 4-connected nets that change the topologyof the parent net. There are three classes of oikodoméic operations: (1) insertion of 2- and 3-connected vertices into 3- and 4-connected plane nets; (2,3) replication of single-layer sheets by topological mirror or two-fold-rotation operators, and condensation of the resulting twosingle-layer sheets to form double-layer sheets. The topological aspects of these sheet structures may be described by functions that express stoichiometry in terms of tetrahedron connectivities (formula-generating functions) and functions that associate these formula-generating functionswith specific two-dimensional nets. Using these functions, we may generate formulae and structural arrangements of single-layer and double-layer silicate structures with specific local and long-range topological features.

Keywords

sheet-silicate mineralsbond topologyformula-generating functionstructure connectivitystructure-generating functionstructure prediction
Type
Frontiers in Theoretical Mineralogy
Information
Mineralogical Magazine , Volume 79 , Issue 7 , December 2015 , pp. 1675 - 1709
Copyright
Copyright © The Mineralogical Society of Great Britain and Ireland 2015

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References

Bakakin, YY, Belov, N.Y, Borisov S.Y and Solov'eva L. P. (1970) The crystal structure of nordite and its relationship to melilite and datolite-gadolinite. American Mineralogist, 55, 1167–1181.Google Scholar
Basso, R., Dal Negro, A., Delia Giusta, A. and Ungaretti, L. (1975) The crystal structure of naujakasite, adouble sheet silicate. Bulletin Gronlands Geologiske Indersogelse, 116, 11–24.Google Scholar
Baur, W.H., Joswig, W., Kassner, D. and Hofmeister, W. (1990) Prehnite: structural similarity of the monoclinic and orthorhombic polymorphs and their Si/Al ordering. Journal of Solid State Chemistry, 86, 330–333.CrossRefGoogle Scholar
Blinov, YA., Voronkov, A.A, Ilyukhin, YY and Belov, N.Y (1975) Crystal structure of lemoynite with a new type of mixed framework. Soviet Physics Doklady, 19, 397–398.Google Scholar
Brualdi, R.A. (1977) Introductory Combinatorics. Elsevier Science, New York.Google Scholar
Camara, K, Sokolova, E., Hawthorne, EC, Rowe, R., Grice, ID. and Tait, K.T. (2013) Veblenite, K2O2Na (Fe|+Fe-+Mn7O)Nb3Ti(Si2O7)2(Si8O22)2O6(OH)10(H2O)3 a new mineral from Seal Lake, Newfoundland and Labrador: mineral description, crystal structure, and a new veblenite (Si8O22) ribbon. Mineralogical Magazine, 11, 2955–2974.CrossRefGoogle Scholar
Cannillo, E., Rossi, G., Ungaretti, L. and Carobbi, S.G. (1968) The crystal structure of macdonaldite. Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti, Serie 8, 45, 399–114.Google Scholar
Cannillo, E., Dal Negro, A. and Rossi, G. (1973) The crystal structure of latiumite, a new type of sheet silicate. American Mineralogist, 58, 466–170.Google Scholar
Capitani, G.C. and Mellini, M. (2006) The crystal structure of a second antigorite polysome (m= 16), by single-crystal synchrotron diffraction. American Mineralogist, 91, 394–399.CrossRefGoogle Scholar
Chakhmouradian, A.R., Cooper, M.A., Ball, N.A., Reguir, E.P., Medici, L., Abdu, YA. and Antonov, A.A. (2014) Vladykinite, Na3Sr4(Fe2+Fe3+)Si8024: A new complex sheet silicate from peralkaline rocks of the Murun complex, eastern Siberia, Russia. American Mineralogist, 99, 235–241.CrossRefGoogle Scholar
Chao, G.Y (1972) The crystal structure of carletonite, KNa4Ca4Si8O18(CO3)4F05(OH)05H2O, a double-sheet silicate. American Mineralogist, 57, 765–778.Google Scholar
Chesnokov, B.Y, Lotova, E.Y, Nigmatulina, E.N., Pavlyuchenko, YS. and Bushmakin, A.F. (1990) Dmisteinbergite CaAl2Si208 (hexagonal) - a new mineral. Zapiski Vsesoyuznogo Mineralogicheskogo Obshchestva, 119, 43–45 [in Russian].Google Scholar
Chukanov, N.Y, Rastsvetaeva, R.K., Aksenov, S.M., Pekov, I.Y, Zubkova, N.Y, Britvin, S.N., Belakovskiy, D.I. andTernes, B. (2012) Giinterblassite, (K,Ca)3_xFe [(Si,Al)13O25(OH,O)4].7(H2O)7, a new mineral: the first phyllosilicate with triple tetrahedral layer. Geology of Ore Deposits, 54, 656–662.CrossRefGoogle Scholar
Chukanov, N.Y, Zubkova, N.Y, Pekov, I.Y, Belakovskiy, D.I., Schiiller, W., Ternese, B., Blass, G. and Pushcharovsky, D.Yu. (2013) Hillesheimite, (K,Ca, O)2(Mg,Fe,Ca,O)2[(Si,Al)13O23(OH)6](OH).8H2O, a new phyllo silicate mineral of the giinterblassite group. Geology of Ore Deposits, 55, 549–557.CrossRefGoogle Scholar
Cohen, D.I.A. (1978) Basic Techniques in Combinatorial Theory. John Wiley and Sons, New York.Google Scholar
Dal Negro, A., Rossi, G. and Ungaretti, L. (1967) The crystal structure of meliphanite. Ada Crystallographica, 23, 260–264.CrossRefGoogle Scholar
Ferraris, G., Khomyakov, A.P., Belluso, E. and Soboleva, S.Y (1998) Kalifersite, a new alkaline silicate from Kola Peninsula (Russia) based on a palygorskite-sepiolte poysomatic series. European Journal of Mineralogy, 10, 865–874.CrossRefGoogle Scholar
Garvie, L.A.J., Devouard, B., Groy, T.L., Camara, F. and Buseck, PR. (1999): Crystal structure of kanemite, NaHSi2O5-3H2O, from the Aris phonolite, Namibia. American Mineralogist, 84, 1170–1175.CrossRefGoogle Scholar
Giustetto, R. and Chiari, C. (2004) Crystal structure refinement of palygorskite from neutron powder diffraction. European Journal of Mineralogy, 16, 521–532.CrossRefGoogle Scholar
Grice, ID. and Hawthorne, EC. (2002) New data on meliphanite, Ca4(Na,Ca)4Be4AlSi7O24(F,O)4 . The Canadian Mineralogist, 40, 971–980.CrossRefGoogle Scholar
Grice, J.D., Rowe, R., Poirier, G., Pratt, A. and Francis, J. (2009) Bussyite-(Ce), a new beryllium silicate mineral species from Mont Saint-Hilaire, Quebec. The Canadian Mineralogist, 47, 193–204.CrossRefGoogle Scholar
Hawthorne, EC. (1983) Graphical enumeration of polyhedral clusters. Ada Crystallographica A39, 724–736.Google Scholar
Hawthorne, EC. (2012) Bond topology and structure-generating functions: Graph-theoretic prediction of chemical composition and structure in polysomatic T-O-T (biopyribole) and H-O-H structures. Mineralogical Magazine, 76, 1053–1080.CrossRefGoogle Scholar
Hawthorne, EC. and Smith, J.Y (1986a) Enumeration of 4-connected 3-dimensional nets and classification of framework silicates. 3-D nets based on insertion of 2-connected vertices onto 3-connected plane nets. Zeitschrift fur Kristallographie, 175, 15–30.Google Scholar
Hawthorne, EC. and Smith, J.Y (19866) Enumeration of 4-connected 3-dimensional nets and classification of framework silicates. Body-centred cubic nets based on the rhombicuboctahedron. The Canadian Mineralogist, 24, 643–648.Google Scholar
Hawthorne, EC. and Smith, J.Y (1988) Enumeration of 4-connected 3-dimensional nets and classification of framework silicates. Combination of zigzag and saw chains with 63, 3.122, 4.82, 4.6.12 and (52.8)2(5.82)! nets. Zeitschrift fur Kristallographie, 183, 213–231.Google Scholar
Hawthorne, EC, Krivovichev, S.Y and Burns, P.C. (2000) The crystal chemistry of sulfate minerals. Pp. 1–112 in: Sulfate Minerals: Crystallography, Geochemistry, and Environmental Significance (C.N. Alpers, J.L. Jambor and D.K. Nordstrom, editors). Reviews in Mineralogy and Geochemistry, 40. Mineralogical Society of America and the Geochemistry society, Washington, DC.Google Scholar
Heaney, P.I, Post, IE. and Evans, H.T. Jr. (1992) The crystal structure of bannisterite. Clays and Clay Minerals, 40, 129–144.CrossRefGoogle Scholar
Johnsen, O., Leonardsen, E.S., Faelth, L. and Annehed, H. (1983) Crystal structure of kvanefjeldite: The introduction of 2(Si3O7OH) layers with eight- membered rings. Neues Jahrbuch fir Mineralogie Monatshefte, 1983, 505–512.Google Scholar
Kampf, A.R., Housley, R.M., Dunning, G.E. and Walstrom, R.E. (2015) Esquireite, BaSi6O13-7H2O, a new layer silicate from the barium silicate deposits of California. The Canadian Mineralogist, DOI: 10.3749/canmin.1400076CrossRefGoogle Scholar
Krivovichev, S.V. (2008) Structural Crystallography of Inorganic Oxysalts. International Union of Crystallography Monographs on Crystallography 22, Oxford University Press.Google Scholar
Krivovichev, S.V. (2009) Structural Mineralogy and Inorganic Crystal Chemistry. St. Petersburg University Press, St. Petersburg, Russia, 398 pp.Google Scholar
Lam, A.E., Groat, L.A., Cooper, M.A. and Hawthorne, F. C (1994) The crystal structure of wickenburgite, Pb3CaAl[AlSiio027](H20)3, a sheet structure. The Canadian Mineralogist, 32, 525–532.Google Scholar
Le Page, Y and Perrault, G. (1976) Structure crystalline de la lemoynite, (Na,K)2CaZr2Sii0O26,5-6(H2O). The Canadian Mineralogist, 14, 132–138.Google Scholar
Liebau, F. (1985). Structural Chemistry of Silicates. Springer-Verlag, Berlin.Google Scholar
Lopes-Vieira, A. and Zussman, L (1969) Further detail on the crystal structure of zussmanite. Mineralogical Magazine, 37, 49–60.CrossRefGoogle Scholar
Mazzi, F, Ungaretti, L. and Dal Negro, A. (1979) The crystal structure of semenovite. American Mineralogist, 64, 202–210.Google Scholar
Mellini, M., Merlino, S. and Rossi, G. (1977) The crystal structure of tuscanite. American Mineralogist, 62, 1114–1120.Google Scholar
Merlino, S. (1972) The crystal structure of zeophyllite. Ada Crystallographica, B28, 2726–2732.Google Scholar
Merlino, S. (1988) Gyrolite: its crystal structure and crystal chemistry. Mineralogical Magazine, 52, 377–387.CrossRefGoogle Scholar
Mikenda, W., Pertlik, F, Povondra, P. and Ulrych, I (1997) On zeophyllite from Radejcin, Ceske stfedohori Mts.: X-ray and IR-investigations. Mineralogy and Petrology, 61, 199–209.CrossRefGoogle Scholar
Papike, II and Zoltai, T (1967) Ordering of tetrahedral aluminum in prehnite, Ca2(Al,Fe3+)[Si3AlOi0](OH)2 . American Mineralogist, 52, 974–984.Google Scholar
Post, IE., Bish, D.L. and Heaney, P.I (2007) Synchrotron powder X-ray diffraction study of the structure and dehydration behavior of sepiolite. American Mineralogist, 92, 91–97.CrossRefGoogle Scholar
Quint, R. (1987) Description and crystal structure of amstallite, CaAl(OH)2[Al0 8Si3 2O8(OH)2]-[(H2O)0 8 Cl0 2], a new mineral from Amstall, Austria. Neues Jahrbuch fur Mineralogie, Monatshefte, 1987, 53–262.Google Scholar
Rastsvetaeva, R.K., Aksenov, S.M. and Chukanov, N.V (2012) Crystal structure of giinterblassite, a new mineral with a triple layer. Doklady Chemistry, 442, 57–62.CrossRefGoogle Scholar
Rumsey, M.S., Welch, M.D., Kampf, A.R. and Spratt, I (2013) Diegogattaite, Na2CaCu2Si8O20-H2O: a new nanoporous copper sheet silicate from Wessels Mine, Kalahari Manganese Fields, Republic of South Africa. Mineralogical Magazine, 77, 3155–3162.CrossRefGoogle Scholar
Sharygin, VV, Pekov, I.Y, Zubkova, N.Y, Khomyakov, A.P., Stoppa, F. and Pushcharovsky, D.Yu. (2013) Umbrianite, K7Na2Ca2[Al3Siio029]F2Cl2, a new mineral species from melilitolite of the Pian di Celle volcano, Umbria, Italy. European Journal of Mineralogy, 25, 655–669.CrossRefGoogle Scholar
Smith, IY (1977) Enumeration of 4-connected 3-dimensional nets and classification of framework silicates; I, Perpendicular linkage from simple hex-agonal net. American Mineralogist, 62, 703–709.Google Scholar
Smith, IY (1978) Enumeration of 4-connected 3-dimensional nets and classification of framework silicates, II, Perpendicular and near-perpendicular linkages from 4.8 , 3.12 and 4.6.12 nets. American Mineralogist, 63, 960–969.Google Scholar
Smith, IY (1988) Topochemistry of zeolites and related materials. I. Topology and geometry. Chemical Reviews, 188, 149–182.CrossRefGoogle Scholar
Subbotin, YY, Merlino, S., Pushcharovskii, D.Yu Pakhomovskii, YA., Ferro, O., Bogdanova, A.Y, Voloshin, A.Y, Sorokhtina, N.Y, Zubkova, N.Y (2000) Tumchaite Na2(Zr,Sn)Si4On-2(H2O) - a new mineral from carbonatites of the Vuoriyarvi alkali-ultrabasic massif, Murmansk region, Russia. American Mineralogist, 85, 1516–1520.CrossRefGoogle Scholar
Takeuchi, Y and Donnay, G. (1959) The crystal structure of hexagonal CaAl2Si208 . Ada Crystallographica, 12, 465–470.CrossRefGoogle Scholar
Welch, M.D. and Rumsey, M.S. (2013) A new naturally-occurring nanoporous copper sheet-silicate with 6482cages related to synthetic “CuSH” phases. Journal of Solid State Chemistry, 203, 260–265.CrossRefGoogle Scholar
Zunic, T.B., Scavnicar, S. and Molin, G. (1990) Crystal structure of prehnite from Komiza. European Journal of Mineralogy, 2, 731–734.CrossRefGoogle Scholar